STUDY ON HAAR WAVELET CONSTRUCTION AND ITS SIMPLE APPLICATION

Wavelet analysis is a new development in the area of applied mathematics and this theory emerges as a powerful tool in modern applied mathematics; The main use of the wavelet theory is that it provides efficient methods for analyzing functions and signals at multiple levels of resolution. Wavelet analysis allows researchers to isolate and manipulate specific types of patterns hidden in masses of data. Wavelet theory is really powerful in applied math, One of the most basic and important wavelet is the Haar Wavelet – It is Very simple, easy to understand and really efficient to use , This Project is all about studying the Haar wavelet, How its Made ,what is can do and how it can be used .By looking at the Haar Wavelet ,We can get a good introduction to the whole idea of Wavelets and how they work .The Goal is to understand the basics of the Haar Wavelet and see how it can be used in different situations . The work in this project is begin with the basic concept of wavelet analysis ,then introduction to the concept of different wavelets ,mainly as Haar Wavelets and Multiresolution Analysis ,Establishing the theoretical foundation which is required to understanding the Haar functions , their construction and their simple application .In this Project we also include the haar function ‘s Construction, how they developed step by step ,Haar Function, Scaling function ,along with their orthogonality ,compact support and simplicity